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Full text of "Analytical Mechanics"

CENTER OF MASS AND MOMENT OF INERTIA    115
y                                               :- -~ r
0
v_>v
FIG. 77. ILLUSTRATIVE EXAMPLE.
Find the center of mass of a paraboloid of revolution obtained by revolving about the ic-axis that part of the parabola y2 = 2 px which lies between the lines x = 0 and x = a.
dm = T7T?/2 dx
 T7T
xdx
FIG. 78.
PROBLEMS.
Find the center of mass of the homogeneous solid of revolution generated by revolving about the x-axis the area bounded by
(1)  y = - x, x = h, and y  0.
(2)  xz = 4 ay, x  0, and y  a.
(3)  a;2 + 2/2 = a2, and x = 0.
(4)   62x2 + a^2 = a262, and x = 0.
(5)  T/ = sinoj, a; = 0, and x = ~-
(6)
+ ?/ == 62, and x = 0.